2022/05/05 by Alex J. Best, L. Alexander Betts, Matthew Bisatt +8 · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic
paper · pdf · doi:10.1112/blms.12604
A new approach has been recently developed to study the arithmetic of hyperelliptic curves (Formula presented.) over local fields of odd residue characteristic via combinatorial data associated to the roots of (Formula presented.). Since its introduction, numerous papers have used this machinery of ‘cluster pictures’ to compute a plethora of arithmetic invariants associated to these curves. The purpose of this user's guide is to summarise and centralise all of these results in a self-contained fashion, complemented by an abundance of examples.